am I allowed to have a go pro while zip lining? if not allowed to have it in my hands, could I strap it to my helmet?

Yes is the short answer. They sell a 5$ phone thingy with strap that worked for me. A go pro would be good too I'm sure, just at your own risk.

You can have your own mount and I was allowed to hold my phone in my hands. Doing so is at your own risk.

Yeah, they have helmets with attachments

Yes

If you can secure it tight on your helmet then yes sure.